Common Knowledge: A Survey
This paper discusses the motivation behind common knowledge. Common knowledge has been argued to be necessary for joint action in general and for language use as a particular kind of joint action. However, this term has been broadly interpreted. Two major issues must be addressed: (1) What mental state corresponds to common knowledge, i.e., is knowledge, belief or supposition the appropriate mental attitude? (2) What inference process allows agents to achieve common knowledge? Most generally, common knowledge is used to describe the knowledge that is evidenced in reflexive reasoning. The term has also been used to refer to facts or objects which are mutually salient. One of the main problems for a theory of common knowledge is whether knowledge is the appropriate mental attitude. It seems as though probabilistic beliefs might approximate the cognitive phenomenon of common knowledge more closely than knowledge. The main problem with a usable notion of common knowledge is that inference must play a critical role in what becomes common knowledge. I discuss the nature of conversational inference. It has a number of properties that distinguish it from other inferential systems, such as being apparently abductive and probabilistic, but a precise characterization of it is an unsolved problem. I suggest that in cases where ensuring common knowledge really matters, participants in dialogue accomplish this is by exploiting opportunities for redundancy in conversation.